Here's the plan: (A) Run a Moorean argument against Subjective Bayesianism, (B) Note that Subjective Bayesians don't have a good reply, (C) Identify some motivations for being a Subjective Bayesian, (D) Note that these motivations are largely meta-normative, and they are satisfied if you're an expressivist Objective Bayesian; (E) Conclude that since expressivist Objective Bayesians can avoid the Moorean argument and satisfy the motivations for Subjective Bayesianism, there is reason for Subjective Bayesians to take this kind of view seriously.

This is a toned down version of a rant to which some of you have already been subjected.

A: Moorean Argument According to Subjective Bayesians, the following are the only norms of rational belief:

Have a Prior: Have a prior that satisfies the probability axioms.

Conditionalize: At all times, let your credences be the result of conditionalizing your prior probability distribution on your total evidence.

Maybe: the prior should satisfy the Principal Principle

Maybe: the prior should be non-dogmatic. (Roughly, unless it is analytic that p, don't have a prior probability of 1 in p. You have to say something else about continuous random variables.)

Objective Bayesians accept all of these constraints, but add constraints that rule out certain prior probability functions. Some Objective Bayesians hold that there is a unique prior that is rationally permissible.

If Subjective Bayesianism is true, then it can be perfectly rational for someone with exactly my evidence to be nearly certain of the following claim:ZOMBIE: flesh-eating zombies are about to descend from the sky and devour us all.* It is irrational to believe ZOMBIE when you have my evidence, so Subjective Bayesianism is false. Nothing the Subjective Bayesian throws at me will be more certain than my main premise, so my argument succeeds.

B: Subjective Bayesian RepliesSome Subjective Bayesians attempt to rebut this kind of argument by appealing to “washing out” theorems. These theorems are of the form “for any n agents whose priors satisfy certain fairly weak conditions, if those agents have a sufficiently long sequence of common observations of a certain kind, then their posterior probabilities will converge”. For instance, if you have two people drawing balls from an urn with replacement, these people satisfy 1-4, they regard the sequence of draws from the urn as exchangeable, and they conditionalize on the result of drawing from they urn, then if they see enough balls drawn from the urn, their estimates of the distribution of colors of balls in the urn will converge.

The first point is that while such theorems might help in some other contexts, they won't help with ZOMBIE. Maybe if someone regarded possible zombie strikes as exchangeable, he'd eventually agree that a zombie strike is unlikely in the near future. But (i) this isn't required by Subjective Bayesianism, and (ii) it would still be irrational to be so damn confident in ZOMBIE (at least) until he stops expecting a zombie strike.

A more entertaining reply to the use of washing out theorems comes from Carnap (though probably others made the same point before him). Although it is true that the opinions of two agents in the urn scenario will converge, the following is also true. For any credence x (0 < x < 1) that the next ball will be red (call this proposition R), for any finite sequence of observations S, there is an exchangeable prior Pr satisfying (1-4) such that Pr(R|S) = x. Put colorfully, if you lined up observers with all possible priors, no matter how long a finite sequence of red draws you had, there'd always be some guy who was 99% confident that the next ball wouldn't be red (and each such guy would be fully rational by Subjective Bayesian standards).

Long story short, I don't think that the washing out stuff mitigates the obvious weirdness of believing a lot of weird stuff, including ZOMBIE.

C: Motivation for Subjective BayesianismWhy have people been so attracted to a view that entails things that are so obviously and irredeemably crazy? I take it there is nothing too weird (at least as an approximation) about having credences that satisfy the probability axioms and updating by conditionalization. The weirdness is entirely due to the paucity of constraints on the priors. So our question is: why go for the Subjective part of Subjective Bayesianism?

Part of the explanation of why some people have gone for this permissive view about priors is that they just mean something especially weighty by words like “irrational”, “unreasonable”, and “unjustified”. They only consider some credences irrational only if they are incoherent, where incoherence is the credence analogue of having inconsistent beliefs. Thus, we had people like Carnap at great pains to argue that the requirement to use his favorite prior was a lot like the requirement to use classical logic.

The idea that these normative notions were especially loaded, so that the two groups were, to some extent, talking past each other might help explain the disagreement. But many (most?) Subjective Bayesians, I take it, think that there is no interesting other way of using these words. So this probably isn't the end of the story.

Subjective Bayesians are, I believe, more significantly motivated by two strands of meta-normative considerations. The first strand is metaphysical: what could make some priors, but not others, rationally permissible? Indifference principles don't work, and the fact that some priors, but not others, are rationally permissible needs explanation. Something has to make it true, and there's no decently natural property that could play the role.

The second strand isepistemic: how could you know that some priors, rather than others, are rationally permissible? Someone who changed his priors after making observations and followed requirement #2 would be Dutch-book-able. So what prior you select can't depend on observation. So if it is knowable that some priors are just plain wrong, it must be a priori that they are just plain wrong. But it's not analytic that certain priors are bad (or anything like that), so it is mysterious how anyone could know whether a given prior was acceptable.

These strands interact with each other: the special property had by the good priors has to be knowable a priori, on pain of us not knowing what it is. So it couldn't be something deeply external. (It couldn't be, for instance, the probability distribution from statistical mechanics, conditional on the past hypothesis.)

That's a bit of a cartoon version of the motivations, but I think it captures the gist of it.

D: How to Meet to Motivations by Going ExpressivistThese objections bear a striking resemblance to Mackie's objections to moral realism. As with Mackie's objections, there are a lot of things you can say here if you don't want to accept the Subjective Bayesian's conclusions. But those who find themselves pushed to Subjective Bayesianism upon considering these issues should take note: an expressivist meta-epistemology with an Objective Bayesian first-order epistemology could accommodate these worries, without endorsing the rational permissibility of crazy beliefs about flesh-eating zombies. On the expressivist line, there's no account of it being true or false that a certain prior is good. There is only an account of what you're doing when you say “That's an irrational prior”, and such. Roughly, you're expressing your commitment to a system of norms that rejects using that prior for belief updating. Thus, you skirt the metaphysical issue about what could make one prior better than another.

What about the epistemic objection? Consider this example:JOHN: John uses the kind of prior that most of us, more or less, endorse. He's been using it since he was a young ideal Bayesian, conditionalizing ever since. John reflects on his use of this prior, considering its justifiability. Since John endorses a system of norms that uses this prior, he says, “I'm glad I used a good prior.” When he sees another guy using the ZOMBIE prior, he adds, “It sure is crazy to be worried about that.”I take it that it is not an essential part of this story that John, behind the scenes, endorsed in some objectionable variety of a priori reflection. So there's no problem here either.**

E: ConclusionIf you're worried about ZOMBIE and you're motivated by the standard arguments for Subjective Bayesianism, Objective Bayesian expressivism might worth looking into. The view will inherit some of the problems of expressivism, but I doubt they will be as bad as endorsing wild beliefs about ZOMBIE.

I think you can run a similar argument against most versions of Humeanism about reasons.

Disclaimer: I don't mean to implicate that I endorse an expressivist version of Objective Bayesianism.

*Technically, you could get out of this by insisting that it is part of my evidence that zombies are not going to fall from the sky and devour us all. You might think, for instance, that we know that this isn't going to happen, and we therefore ought to have conditionalized on the claim that it won't happen. This sort of reply is short-sighted though. Just insert some other example of something that clearly merits little credence, given our present evidence, but is not entailed by our present evidence. (E.g., we'll all die at the hands of nuclear terrorists within the next two years.) For rhetorical purposes, I will stick to talking about flesh-eating zombies.

**Things may be a bit trickier than this. It isn't especially clear, even if expressivism is true, how you're supposed to get your normative beliefs. However, even if it is true that expressivists like John who go around using good priors are somehow engaging in an objectionable variety of a priori reasoning, what is really crazier to believe at the end of the day: (i) it is rationally permissible to use a priori reasoning to select a prior, or (ii) it is rationally permissible for someone with my evidence to expect flesh-eating zombies to fall from the sky and devour us all? At any rate, appeal to expressivism helps here at least as much as it helps in meta-ethical contexts.